Establishing the Molecular Point Group

If the molecule does not belong to one of these special groups, a systematic approach is followed. Firstly, the possible presence of rotation axes in the molecule is checked. If there is no rotation axis, then it is determined 

In any case the search is for the highest order C axis. Then it is ascertained whether there are Cj axes present perpendicular to the C axis. If such Cj axes are present, then there is D symmetry. If in addition to D symmetry there is a cr plane, the point group is while if there are n symmetry planes (erj bisecting the twofold axes, the point group is If there are no symmetry planes in a molecule with D symmetry, the point group is D . 

Finally, if no Cj axes perpendicular to C are present, then the lowest symmetry will be C when a perpendicular symmetry plane is present, the point group will be and when there are n coinciding symmetry planes, it will be C . 

In this section, actual molecular structures are shown for the various point groups along with occasional examples from outside chemistry. The Schoen-flies notation is used and the characteristic symmetry elements are enumerated. 

One fourfold rotation axis and four twofold rotation axes which are perpendicular to the fourfold axis. The four axes are grouped in two nonequivalent pairs. One pair is rotated relative to the other pair by 45°. The angle between the two axes within each pair is 90°. 

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Figure 3-5 shows a possible scheme for establishing the molecular point group that has been widely used to reliably establish molecular symmetries [9],... 

Figure 3-5. Scheme for establishing the molecular point groups (cf. Refs. [3-4] and [3-5]). 

A diagram of the geometry and axis conventions for ketene is shown in Fig. 36. The molecule has a planar structure with symmetry. The molecular orbitals in the ketene molecule are not directly analogous to those of formaldehyde, as was recognized in early ab initio studies Ketene is a 22 electron system with 16 valence electrons. The molecular orbitals can be classified according to their behavior under the symmetry operations of the molecular point group, C, . Detailed MO calculations have established that the ground state orbital occupancy is ... 

X-Ray.—The crystal and molecular structure of tri-o-tolylphosphine, its oxide, sulphide, and selenide (125) have been compared. The mean P—C bond lengths appear to be determined by the n-electron density along the P—C bond and intramolecular steric interactions, d-Orbital participation was considered to be of little importance.152 X-Ray diffraction established the structure of diphosphinofumarate (126)153 and showed that the phospholanium iodide (127) has an envelope ring with the methyl group at the point of the flap.154 The bicyclic phosphonium bromide (128) has a distorted half-chair phosphorus-containing ring, one of the P—C bonds in the... 

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